The practice was uncovered by inspectors during a focused visit to Oldham children's services in March, looking into their initial response to child protection concerns.
Inspectors said the screening visits are being carried out outside of the formal single assessment process, meaning that families are being assessed without their knowledge and without rights to read, comment or have their views recorded.
Ofsted said that there was no clear reason for the visits, which in some instances led to cases being delayed.
Oldham Council has pledged to review the use of the screening visits on the back of Ofsted's concerns.
"The local authority explained that these visits are an assessment," states a letter outlining Ofsted's findings to the council.
"However, they are undertaken outside of the single assessment process and this means that families are being assessed without their knowledge or right to read, comment and have their views recorded, and this is unacceptable.
"In some cases, these visits led to a delay in children having their needs formally assessed and also meant that children and their families had to explain their circumstances to more than one worker in quick succession."
Despite the concerns, inspectors praised the swift response children and young people in need of support received via the council's "front door" services.
Information sharing by partners, co-located in the multi-agency safeguarding hub, which deals with initial child protection concerns, was found to be effective.
Meanwhile, thresholds for support were found to be applied well and managers' oversight of work is described as being detailed.
Assessments of cases were found to be of a high quality but Ofsted said it wants to see these give a greater prominence to children's histories to further assess whether they are at risk.
Inspectors were also impressed with the early intervention services offered to families, covering issues such as managing challenging behaviour and truancy.
"Children and families who need some additional support have access to a wide range of well-developed early help services," Ofsted's letter adds.
"Those children and their families requiring more intensive early help support receive a good service that results in improved outcomes, such as increased attendance at school, less conflict in the home and more parental confidence in managing their child's behaviours."
This is the second time in six months that Ofsted has branded practice in the support of vulnerable children in Oldham as "unacceptable".
In November last year a joint inspection by Ofsted and health watchdog the Care Quality Commission raised concerns about the quality of education, health and care plans for children with special educational needs and disabilities.
In 2015 Oldham council's children's services were rated as "requires improvement" by Ofsted following a single inspection.
Jenny Harrison, Oldham Council's cabinet member for safeguarding and social care, said: "We welcome the findings of Ofsted's focused visit and are pleased they have acknowledged our areas of strength and highlighted examples of good practice.
"We're particularly pleased that Ofsted found the majority of children in need of urgent help and protection are identified and receive a swift and effective multi-agency response. Some staff were also praised for their creative direct work with children and young people.
"The recommendations for improvement are in areas we're already addressing and we will continue that work with partners because providing vital and effective services for Oldham's children and families in need is a key priority for us."